Android Auto is designed to limit distractions, so it won't ping you with every notification on your phone. It can still be enough to get annoying, though. Google is finally addressing that with the option to silence notifications in Android Auto.
When you turn off your notification sounds, you will be able to enjoy audio in the car without being interrupted for each message. You'll find the new toggle in the Android Auto settings. It's labeled "No sound from notifications." So, that's pretty self-explanatory. Or rather, it should be.
It looks like Google introduced a strange bug with this feature. The notifications don't produce sound, but they still pop-up on the screen, and they don't go away until you swipe them. Hopefully, that gets addressed soon.